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# If m and k are integers, is x an integer?

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If m and k are integers, is x an integer? [#permalink]

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23 Feb 2016, 18:34
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If $$m$$ and $$k$$ are integers, and $$x^m = k$$, is $$x$$ an integer?

(1) $$-1 < k <2$$
(2) $$m > 0$$
[Reveal] Spoiler: OA

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If m and k are integers, is x an integer? [#permalink]

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24 Feb 2016, 03:49
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TeamGMATIFY wrote:
If $$m$$ and $$k$$ are integers, and $$x^m = k$$, is $$x$$ an integer?

(1) $$-1 < k <2$$
(2) $$m > 0$$

hi,

$$x^m = k$$, m and k are integers, is x an integer..

(1) $$-1 < k <2$$
since k is an integer, k=0 or 1..
so
1) x^m=0
here x will be 0 as m is an integer
or x^m=1..
here it is possible x is a fraction or non integer while m=0, and x is an integer 1, with m as any integer..
insuff

(2) $$m > 0$$
m can be any integer greater than 0, but we do not know anything about k..
m acn be 2 and x $$\sqrt{3}$$, then k will be an integer..
or m=2 and x =3 , here k will again be an integer..
so x can be a non integer or integer..
insuff.

combined..
we know m>0, so x^m=1, only when x is 1..
Suff..

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Re: If m and k are integers, is x an integer? [#permalink]

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24 Feb 2016, 22:31
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If m and k are integers, and x^m=k , is x an integer?

(1) −1<k<2
(2) m>0

In the original condition, there are 3 variables(x,k,m) and 1 equation(x^m=k), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), if k is an integer not x, k=0,1, which only satisfies 1^m=1, 0^m=0. So, it is yes and sufficient.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If m and k are integers, is x an integer? [#permalink]

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21 Oct 2017, 13:45
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Re: If m and k are integers, is x an integer?   [#permalink] 21 Oct 2017, 13:45
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